The velocity of any mechanical wave, whether transverse or longitudinal, depends both on the inertial properties of the medium (to store kinetic energy) and its elastic properties (to store potential energy). Thus, we can write, generically, that the velocity of a wave is given by:
\(v = \sqrt{\frac{\text{elastic property}}{\text{inertial property}}} \)
The speed of a wave is independent of the movement of the source relative to the medium.
It is given by
\( v = \sqrt{ \frac{T}{\mu} } \)
A wave function y(x, t) describes the displacement of individual particles from the medium. For a sine wave traveling in the positive x direction, we have:
The power transmitted by any harmonic wave is proportional to the square of the frequency and to the square of the amplitude. On a string, the expression is:
\( P = \frac{\mu \omega^2 A^2 v}{2} \)